New binary quantum stabilizer codes from classical quasi-cyclic codes of index two

doi:10.1088/1674-1056/ae067b

Abstract We study the algebraic structures of a generalized class of quasi-cyclic codes of index two, and prove that any quasi-cyclic code of index two can be transformed into our proposed quasi-cyclic codes. We determine the generator forms of the proposed quasi-cyclic codes and their Hermitian dual codes. We establish the necessary and sufficient conditions for Hermitian self-orthogonality and dual-containing property to construct quantum stabilizer codes via the Hermitian construction method. As an application, 10 record-breaking quantum stabilizer codes are constructed.

Keywords: quasi-cyclic codes quantum stabilizer codes Hermitian inner product Hermitian construction

Received: 11 July 2025
Revised: 10 September 2025
Accepted manuscript online: 15 September 2025

PACS:	03.67.-a	(Quantum information)
	03.67.Pp	(Quantum error correction and other methods for protection against decoherence)
	89.70.Kn	(Channel capacity and error-correcting codes)

Fund: This research was funded by the National Natural Science Foundation of China (Grant No. 61372072), the Overseas Expertise Introduction Project for Discipline Innovation (111 Project) (Grant No. B08038), and the Fundamental Research Funds for the Central Universities.

Corresponding Authors: Zhuo Li
E-mail: lizhuo@xidian.edu.cn

Cite this article:

Zhen-Hui Zhang(张镇辉), Zhuo Li(李卓), and Li-Juan Xing(邢莉娟) New binary quantum stabilizer codes from classical quasi-cyclic codes of index two 2026 Chin. Phys. B 35 040303

[1] Arute F, Arya K, Babbush R, et al. 2019 Nature 574 505
[2] Knill E, Laflamme R and Zurek W H 1998 Science 279 342
[3] Gottesman D 1997 Stabilizer codes and quantum error correction (California Institute of Technology)
[4] Du C, Ma Z and Xiong M 2023 Chin. Phys. B 32 050307
[5] Hong H Y, Lu X J and Kuang S 2023 Chin. Phys. B 32 040603
[6] Xiao B, Fan Z X, Sun H Q, Ma H Y and Fan X K 2025 Chin. Phys. B 34 050306
[7] Krinner S, Lacroix N, Remm A, et al. 2022 Nature 605 669
[8] Steane A 1996 Physical and Engineering Sciences 452 2551
[9] Steane A M 1999 IEEE Transactions on Information Theory 45 2492
[10] Calderbank A R, Rains E M, Shor P M and Sloane N J 1999 IEEE Transactions on Information Theory 44 1369
[11] Ketkar A, Klappenecker A, Kumar S and Sarvepalli P K 2006 IEEE Transactions on Information Theory 52 4892
[12] Kasami T 1974 IEEE Transactions on Information Theory 20 679
[13] Ling S and Sole P 2003 IEEE Transactions on Information Theory 49 1052
[14] Siap I, Aydin N and Ray-Chaudhuri D K 2000 IEEE Transactions on Information Theory 46 1554
[15] Daskalov R and Hristov P 2003 IEEE Transactions on Information Theory 49 3001
[16] Chen E Z 2018 Journal of Algebra Combinatorics Discrete Structures and Applications 20 65
[17] Akre D, Aydin N, Harrington M J and Pandey S R 2021 arXiv:2108.10316
[18] Galindo C, Hernando F and Matsumoto R 2018 Finite Fields and Their Applications 52 261
[19] Lv J, Li R and Wang J 2019 IEEE Access 7 85782
[20] Lv J, Li R and Wang J 2020 IEEE Communications Letters 24 1067
[21] Guan C, Li R, Lu L, Liu Y and Song H 2022 Quantum Inf. Processing 21 263
[22] Guan C, Li R and Ma Z 2022 arXiv:2212.14225
[23] Abdukhalikov K, Bag T and Panario D 2023 Discrete Mathematics 346 113369
[24] Guan C, Li R, Lv J and Ma Z 2024 IEEE Transactions on Information Theory
[25] Lally K and Fitzpatrick P 2001 Discrete Applied Mathematics 111 157
[26] BosmaW, Cannon J and Playoust C 1997 Journal of Symbolic Computation 24 235
[27] Grassl M 2007 http://www.codetables.de, Accessed on 2025-07-11

[1]	Encoding entanglement-assisted quantum stabilizer codes Wang Yun-Jiang(王云江), Bai Bao-Ming(白宝明), Li Zhuo(李卓), Peng Jin-Ye(彭进业), and Xiao He-Ling(肖鹤玲) . Chin. Phys. B, 2012, 21(2): 020304.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

New binary quantum stabilizer codes from classical quasi-cyclic codes of index two

Cite this article:

Online attention